Our study is motivated by the fact that over the last few years several papers[1]}, [2]}, [3]}, [4]} have independently reported that vertices in the inner shells of the networks can be leveraged to identify high centrality nodes or serve as seeds for community detection. However, each paper focused on only one type of analysis and there was rarely any overlap between the networks studied in these papers. When we conducted an integrated study over a large set of real-world and synthetic networks, we observed that the reported properties of the vertices in the inner shells hold only for a certain type of networks. This observation impelled us to investigate the topological property of networks where the inner shells contain high centrality nodes.
